Uniqueness results in the inverse scattering problem for periodic structures. (English) Zbl 1236.35207
Summary: This paper is concerned with the inverse electromagnetic scattering by a 2D (impenetrable or penetrable) smooth periodic curve. Precisely, we establish global uniqueness results on the inverse problem of determining the grating profile from the scattered fields corresponding to a countably infinite number of quasiperiodic incident waves. For the case of an impenetrable and partially coated perfectly reflecting grating, we prove that the grating profile and its physical property can be uniquely determined from the scattered field measured above the periodic structure. For the case of a penetrable grating, we show that the periodic interface can be uniquely recovered by the scattered field measured only above the interface. A key ingredient in our proofs is a novel mixed reciprocity relation that is derived in this paper for the periodic structures and seems to be new.
MSC:
| 35R30 | Inverse problems for PDEs |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 35Q61 | Maxwell equations |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
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